Journal of Operator Theory

Volume 56, Issue 2, Fall 2006 pp. 391-402.

The lattice of closed ideals in the Banach algebra of operators on a certain dual Banach space

Authors: Niels Jakob Laustsen

$1$ , Thomas Schlumprecht

$2$ , and Andras Zsak

$3$
Author institution:

$1$ Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK--2100 Copenhagen, Denmark and Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England

$2$ Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

$3$ Department of Mathematics, Texas A&M University, College Station, TX 77843, USA, and Fitzwilliam College, Cambridge CB3 0DG, England

Summary: We determine the closed operator ideals of the Banach space

$\begin{equation*} (\ell_2^1\oplus\ell_2^2\oplus\cdots\oplus \ell_2^n\oplus\cdots)_{\ell_1}. \end{equation*}$

Keywords: Ideal lattice, operator, Banach space, Banach algebra.

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